Dephasing-induced Quantum Hall Criticality in the Quantum Anomalous Hall system

Conventional wisdom holds that static disorder is indispensable to the integer quantum Hall effect, underpinning both quantized plateaus and the plateau-plateau transition. We show that pure dephasing, without elastic disorder, is sufficient to generate the same $\theta$ driven criticality. Starting from a Keldysh formulation, we derive an open system nonlinear $\sigma$ model (NL$\sigma$M) for class A with a topological $\theta$ term but no Cooperon sector, and we demonstrate that nonperturbative instantons still govern a two parameter flow of $(\sigma_{xx},\sigma_{xy})$. Evaluating $\theta$ in a dephasing quantum anomalous Hall setting, we predict a quantum Hall critical point at $\sigma_{xy}=1/2$ with finite $\sigma_{xx}$ the hallmark of the integer quantum Hall universality class realized without Anderson localization. Boundary driven simulations of the Qi_Wu_Zhang model with local dephasing confirm this prediction and provide an experimentally aligned protocol to extract $(\sigma_{xx},\sigma_{xy})$ from Hall potential maps. By establishing dephasing as a self contained route to Hall criticality, our framework reframes plateau physics in open solid state and cold atom platforms and offers practical diagnostics for topological transport in nonunitary matter.